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EXISTENCE RESULTS FOR ABSTRACT DEGENERATE NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

Part of: Functional-differential and differential-difference equations Miscellaneous topics - Partial differential equations

Published online by Cambridge University Press:  13 January 2010

EDUARDO HERNÁNDEZ  and
KRISHNAN BALACHANDRAN
EDUARDO HERNÁNDEZ*
Affiliation:
Departamento de Matemática, I.C.M.C. Universidade de São Paulo, Caixa Postal 668, 13560-970 São Carlos SP, Brazil (email: [email protected])
KRISHNAN BALACHANDRAN
Affiliation:
Department of Mathematics, Bharathiar University, Coimbatore 641046, India (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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In this paper we discuss the existence of solutions for a class of abstract degenerate neutral functional differential equations. Some applications to partial differential equations are considered.

Keywords

neutral equationsmild solutionssemigroup of bounded linear operators

MSC classification

Secondary: 35R10: Partial functional-differential equations 34K40: Neutral equations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 81 , Issue 2 , April 2010 , pp. 329 - 342
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

References

[1]Adimy, M. and Ezzinbi, K., ‘A class of linear partial neutral functional-differential equations with nondense domain’, J. Differential Equations 147(2) (1998), 285–332.CrossRefGoogle Scholar
[2]Balachandran, K. and Sakthivel, R., ‘Existence of solutions of neutral functional integrodifferential equation in Banach spaces’, Proc. Indian Acad. Sci. Math. Sci. 109(3) (1999), 325–332.CrossRefGoogle Scholar
[3]Balachandran, K., Shija, G. and Kim, J. H., ‘Existence of solutions of nonlinear abstract neutral integrodifferential equations’, Comput. Math. Appl. 48(10–11) (2004), 1403–1414.CrossRefGoogle Scholar
[4]Benchohra, M., Henderson, J. and Ntouyas, S. K., ‘Existence results for impulsive multivalued semilinear neutral functional differential inclusions in Banach spaces’, J. Math. Anal. Appl. 263(2) (2001), 763–780.CrossRefGoogle Scholar
[5]Benchohra, M. and Ntouyas, S. K., ‘Nonlocal Cauchy problems for neutral functional differential and integrodifferential inclusions in Banach spaces’, J. Math. Anal. Appl. 258(2) (2001), 573–590.CrossRefGoogle Scholar
[6]Cannarsa, P. and Sforza, D., ‘Global solutions of abstract semilinear parabolic equations with memory terms’, Nonlinear Differ. Equat. Appl. 10(4) (2003), 399–430.CrossRefGoogle Scholar
[7]Clément, P. and Nohel, J. A., ‘Asymptotic behavior of solutions of nonlinear Volterra equations with completely positive kernels’, SIAM J. Math. Anal. 12(4) (1981), 514–535.CrossRefGoogle Scholar
[8]Clément, P. and Prüss, J., ‘Global existence for a semilinear parabolic Volterra equation’, Math. Z. 209(1) (1992), 17–26.CrossRefGoogle Scholar
[9]Datko, R., ‘Linear autonomous neutral differential equations in a Banach space’, J. Differential Equations 25(2) (1977), 258–274.CrossRefGoogle Scholar
[10]Dauer, J. P. and Balachandran, K., ‘Existence of solutions of nonlinear neutral integrodifferential equations in Banach spaces’, J. Math. Anal. Appl. 251(1) (2000), 93–105.CrossRefGoogle Scholar
[11]Fang, H. and Li, J., ‘On the existence of periodic solutions of a neutral delay model of single-species population growth’, J. Math. Anal. Appl. 259(1) (2001), 8–17.Google Scholar
[12]Freedman, H. I. and Kuang, Y., ‘Some global qualitative analyses of a single species neutral delay differential population model. Second Geoffrey J. Butler Memorial Conference in Differential Equations and Mathematical Biology (Edmonton, AB, 1992)’, Rocky Mountain J. Math. 25(1) (1995), 201–215.CrossRefGoogle Scholar
[13]Granas, A. and Dugundji, J., Fixed Point Theory (Springer, New York, 2003).CrossRefGoogle Scholar
[14]Gurtin, M. E. and Pipkin, A. C., ‘A general theory of heat conduction with finite wave speed’, Arch. Ration. Mech. Anal. 31 (1968), 113–126.CrossRefGoogle Scholar
[15]Hale, J. K. and Verduyn Lunel, S. M., Introduction to Functional-Differential Equations, Applied Mathematical Sciences, 99 (Springer, New York, 1993).CrossRefGoogle Scholar
[16]Hernández, E., ‘Existence results for partial neutral integrodifferential equations with unbounded delay’, J. Math. Anal. Appl. 292(1) (2004), 194–210.CrossRefGoogle Scholar
[17]Hernández, E. and Henríquez, H., ‘Existence results for partial neutral functional differential equation with unbounded delay’, J. Math. Anal. Appl. 221(2) (1998), 452–475.CrossRefGoogle Scholar
[18]Hernández, E. and O’Regan, D., ‘Existence results for abstract partial neutral differential equations’, Proc. Amer. Math. Soc. 137 (2009), 3309–3318.CrossRefGoogle Scholar
[19]Henríquez, H. R., ‘Regularity of solutions of abstract retarded functional-differential equations with unbounded delay’, Nonlinear Anal. 28(3) (1997), 513–531.CrossRefGoogle Scholar
[20]Kuang, Y., ‘Qualitative analysis of one- or two-species neutral delay population models’, SIAM J. Math. Anal. 23(1) (1992), 181–200.CrossRefGoogle Scholar
[21]Li, Q., Cao, J. and Wan, S., ‘Positive periodic solution for a neutral delay model in population’, J. Biomath. 13(4) (1998), 435–438.Google Scholar
[22]Lunardi, A., ‘On the linear heat equation with fading memory’, SIAM J. Math. Anal. 21(5) (1990), 1213–1224.CrossRefGoogle Scholar
[23]Nunziato, J. W., ‘On heat conduction in materials with memory’, Quart. Appl. Math. 29 (1971), 187–204.CrossRefGoogle Scholar
[24]Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, 44 (Springer, New York, 1983).CrossRefGoogle Scholar